At a certain company all Type A printers work at one constant rate and all Type B printers work at another constant rate. If 12 Type A printers print 840000 pages in 8 hours and 8 Type B printers print 720000 pages in 8 hours what is the total number of pages that 4 Type A and 3 Type B printers will print together in 12 hours?

Rationale

4 Type A and 3 Type B printers will print a total of 825,000 pages together in 12 hours.

To find the total number of pages printed by 4 Type A and 3 Type B printers in 12 hours, we first calculate the printing rates of each printer type and then apply these rates to the specified quantities and time.

A (550000) YOUR ANSWER

This choice underestimates the total output. When calculating the combined printing capacity of 4 Type A and 3 Type B printers, the derived total exceeds this value based on their respective rates.

B (625000) YOUR ANSWER

This answer also falls short of the actual total. The calculation for the number of pages printed by both printer types in 12 hours reveals a significantly higher output than this figure.

C (700000) YOUR ANSWER

While this number is closer to the calculated outputs, it still does not account for the full printing capacity of 4 Type A and 3 Type B printers over the 12-hour period, leading to an underestimation.

D (775000) YOUR ANSWER

This option is a miscalculation that approaches the correct total but still does not encompass the complete printing capabilities of the specified number of printers. The output exceeds this number based on the rates derived from the initial data.

E (825000) CORRECT

This choice correctly represents the total number of pages printed by 4 Type A and 3 Type B printers in 12 hours. The calculations demonstrate that both types of printers contribute significantly to the total output, achieving this exact figure.

Conclusion

In summary, by calculating the individual printing rates and applying them to the given quantities and time, we find that 4 Type A and 3 Type B printers together produce 825,000 pages in 12 hours. This systematic approach confirms that option E is the only accurate solution reflecting the combined printing capacity of both printer types.

4 Type A and 3 Type B printers will print a total of 825,000 pages together in 12 hours.

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